If Chief Executive Officer Akbar Al Baker could pull it off, such a deal would solve several problems for the company and for Qatar itself.

The unified front the big three U.S. carriers have formed against the Gulf's airlines could be fractured, giving Al Baker a chance to nose ahead of Emirates and Etihad Airways PJSC in adding flights to North America. A voice in the U.S. aviation market might help address other thorny issues, such as the laptop ban and visa restrictions for travelers from Middle Eastern countries imposed by President Donald Trump's administration.

Flying High

International traffic by Qatar Airways has grown to outstrip that of American Airlines

Beyond that, the CEO could plug the North Atlantic gap between the networks of Qatar's other two major equity alliance partners, IAG SA (the owner of British Airways) and Latam Airlines Group SA. And, as the tiny emirate sweats under a blockade by four Arab states demanding that it cut ties with Iran and shutter its Al Jazeera television network, a $2.4 billion-odd investment would do no harm in burnishing Qatar's image in the U.S.

That's not to mention the potential financial benefits, now that full-service aviation in the U.S. has been more or less stitched up between American, Delta Air Lines Inc. and United Continental Holdings Inc. American still trades at a discount to the S&P 500 Airlines Index, after all.

Value of 10% stake in American

$2.4 billion

There's a problem with Hail Mary passes, though: If you fumble the ball, you're in trouble.

That seems to have been the outcome of Al Baker's gambit. Far from welcoming his potential new shareholder, American's CEO, Doug Parker, described the move as "puzzling at best and concerning at worst," while the carrier's feisty pilots union described it as an act of "financial aggression." In a country where Alcoa Inc.'s chief executive was ousted in April over a discourteous letter to an activist shareholder, that's a remarkably brusque way to confront a possible major investor.

Marginal Benefit

Now it's making money, American Airlines is far more profitable than Qatar Air

One mistake was to misread the way the wind is blowing in Fort Worth and Washington. Far from being in a position to offer Qatari partners a foot in the door of the administration, American Airlines these days is likely to be more worried about attracting a Twitter thunderbolt from the Oval Office and further sallies from its unions.

After Parker criticized Trump's travel ban and skipped a February meeting with the president, things had been going more smoothly of late, with House Republicans proposing a carrier-friendly bill to privatize air-traffic control. As U.S. airlines are united in their pursuit of policy concessions, the last thing Parker needs is to attract the reputation of a fifth columnist in the pay of Gulf rivals.

There's a more fundamental error, though. Equity stakes such as the one proposed by Al Baker can be more than just symbolic: American Airlines itself only just bought a $200 million share of China Southern Airlines Co. in a move that looks like an attempt to solve some of Parker's problems getting decent slots at Chinese airports. But they work best when the carriers are in a positive-sum game, where the benefits of cooperation can be shared between both sides.

Charity Begins at Home

American Airlines' passenger yields are already declining on international routes. It doesn't need more competition

Source: Bloomberg

Note: RPM=revenue passenger miles, the number of passengers carried multiplied by the distance they've been carried. Yields represent passenger revenue per RPM.

Qatar isn't in that position. Unlike China, which has a huge and fast-growing market to which American wants better access, it has very little to offer Parker beyond its investment. American doesn't have eastbound flights that go further than Athens, so it doesn't appear to be holding out for a share of Middle East traffic. While the carriers have a code-share deal via the Oneworld alliance, deepening that relationship would only put downward pressure on international passenger yields that are already at a seven-year low.

In its diplomatic battle with Arab rivals, Qatar is finding it difficult to take on a group that's pressing its advantage with the perceived backing of the U.S. president. In his struggle with America's revanchist airlines, Al Baker is finding that aviation isn't all that different.

This column does not necessarily reflect the opinion of Bloomberg LP and its owners.

David Fickling is a Bloomberg Opinion columnist covering commodities, as well as industrial and consumer companies. He has been a reporter for Bloomberg News, Dow Jones, the Wall Street Journal, the Financial Times and the Guardian.